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January 29th, 2013, 05:09 AM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  prove inequality satisfying :a+b+c=0 and , abc=8 prove : 
January 29th, 2013, 05:13 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: prove inequality
Without loss of generality, let a <= b <= c. We must have a < b < 0 and so a < c and so 1/a + 1/c < 0 and hence 1/a + 1/b + 1/c < 0. 
January 29th, 2013, 05:19 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  Re: prove inequality 
January 29th, 2013, 06:48 AM  #4 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: prove inequality
greg1313: very good solution 

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